Abstract
It is considered an extended notion of the commutativity of the encryption. Using the computational difficulty of the hidden discrete logarithm problem, a new method and post-quantum probabilistic algorithm for commutative encryption are proposed. The finite non-commutative associative algebra containing a large set of the global left-sided unites is used as the algebraic carrier of the proposed method and probabilistic commutative cipher. The latter is secure to the known-plaintext attack and, therefore, efficient to implement on its base a post-quantum no-key encryption protocol. Main properties of the algebraic carrier, which are used in the commutative encryption method, are described.
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